## High Resistance Measurement## Updated 4 November 2024Fertiliser Resistivity Probe
## IntroductionThe photo above shows a Probe for measuring the resistivity of granular fertiliser. Resistivity is defined below as the resistance observed, times a cell constant. The design could be adapted for many other applications. With powdered or granular materials the probes are fully inserted into the sample and the switch is then turned on. After a delay the LED might light up. The delay time is proportional to the resistance of the sample.
## Features- A resistance range from 100,000,000 ohms to about 100,000,000,000 ohms can be measured in a time varying from about 1 second to 1000 seconds
- The maximum Probe power supply current, with the LED on, is less than 300 microamps. Before the LED turns on it is less than 10 microamps.
- The probes are stainless steel chop-sticks.
- The LED is a modified Christmas light which has a strong output at a very low current. I have not found any commercial source which is better.
## PrincipleThe device is essentially a one-bit computer (a high input impedance electronic switch) connected to the output of an analog current-integrator. The integrator input is connected to one of the electrodes. A 3 volt CR2032 lithium cell powers the circuit and is connected to the other electrode. If the sample is slightly conductive a current passes between the electrodes into a 10 nanofarad integrating capacitor. When the charge on the capacitor reaches a threshold, determined by the circuit, the green/white LED will turn on. The time taken for the LED to turn on is proportional to the resistance of the sample. A sample with a resistance of 2,000,000,000 ohms, between the electrodes, will take about 19.5 seconds to turn the LED on. This time will vary between circuits because of component tolerences. Measuring the highest resistances with a meter would probably require some shielding from electrical noise. An integrator performs better. ## Non-Linear SamplesWhen an insulation tester is used to measure samples which are slightly acidic, like superphosphate fertiliser, it does not represent the initial state of the sample. With 100 to 1000 volts applied the sample rapidly charges up to the applied voltage where little current will flow. Once the reading is stable the value is recorded. Initially there is a substantial pulse of current until the sample equilibrates. By the time the sample has adapted, the resistance is measured as being very high. The sample is not a pure resistance. The pulse is much stronger than the polarisation due to capacitance that occurs with normal insulators. A rough model of this sample type is an electrolytic capacitor in parallel with a high resistance. The residual acid and the stainless steel electrodes makes a crude electrolytic capacitor. Little current flows once the electrolytic capacitor voltage rises to match the applied voltage. The Probe measurement more closely represents the initial undisturbed state of the sample. ## Resistivity
For bulk samples the resistance measured is expressed as resistivity.
Resistivity = resistance x electrode area / electrode spacing.
Resistivity is a bulk property which is independent of the electrode geometry.
The electrode area / electrode spacing is called the cell constant.
The cell constant unit is metre For safe handling of some powdered or granulated samples an upper resistivity limit is set, 1E9 ohm metre for example. Above this value fires or clogging could occur during sample handling. For the probe the cell constant is approximately 0.2 metre. At the resistivity limit the resistance measured is 5E9 ohms. ## Improvements- Teflon electrode sleeves could be added to improve the performance at high resistances.
- A red LED could be added to turn on when a defined resistivity threshold is reached, for example 1E9 ohm metre.
- The present circuit could be turned into an oscillator along with a 12 stage counter added. This would allow wide resistance ranges to be measured. A 12 position switch would double the number of integration cycles for each step. 4096 cycles would allow resistances lower than 100 kohm to be measured. A single cycle with a 1 nanofarad integrating capacitor would allow resistances around 1E12 ohms to be measured. The LED would be connected to the selected counter output.
- The now positive output of the counter would be fed back to the ground pin of the oscillator, to stop the counting and to keep the LED on.
## Other Methods for Measuring High ResistancesThere are numerous ways to measure high resistances. Typically, insulation testers are adapted for this purpose. For high resistances the applied voltage may range from 100 volts to over 1000 volts. Electrode assemblies can have an increased surface area with a reduced spacing for some high resistance measurements. Electrical sheilding and guard circuits are required for the highest resistances. Insulation testers are available from most manufacturers of digital multimeters. Some can measure resistances into the teraohm range but only with a completely shielded setup. Apart from the insulation testers, a basic digital multimeter and a DC power supply can be used to measure very high resistances. The multimeter voltage ranges typically have a 1E7 ohm input resistance. The lowest voltage range can be used to measure small currents. I do have a meter with a 22,000,000,000 ohm input resistance on the lowest range. This may be useful for some applications or a 1E7 ohm shunt resistor can be added. A 1E7 ohm input resistance UNI-T UT33B multimeter, a 10 volt DC power supply and a series resistance of 1E10 ohms produces a meter reading of 10.0 mV. ## Measuring the Resistivity of a Memo Cube Paper StackI used a full stack of Memo Cube paper as a test sample with two 52 mm diameter electrodes and a 1.6 kilogram weight compressing the electrodes onto the stack. In this case the cell constant is derived from a cylindrical cell matching the diameter of one of the electrodes with a length equal to the thickness of the paper stack. - The measured voltage in series with the stack was 0.0105 volts.
- The multimeter input resistance was 1E7 ohms.
- The current was 0.0105/1E7 = 1.05E-9 amps.
- The voltage across the stack of paper was 10 - 10.5E-3 = 9.99 volts.
- The paper stack resistance is 9.99 / 1.05E-9 = 9.514E9 ohms.
- The area of the electrode = (5.2E-2 /2)
^{2}x 3.14159 = 2.12E-3 square metres. - The Memo Cube thickness is 3.55E-2 metres.
- The resistivity is 9.514E9 x 2.12E-3 / 3.55E-2 =
**5.68E8 ohm metre.**
The Memo Cube resistivity measured with the probe connected to the electrodes was 1.18E10 ohms x 2.12E-3 /3.55E-2 = We know that 2,000,000,000 ohms takes about 19.5 seconds before the LED turns on. With the Memo Cube paper stack the time delay was 115 seconds. 2E9 ohms x 115 / 19.5 = 1.18E10 ohms. The experimental work described here was done at a relative humidity of 70% and a temperature of 20 degrees Celsius. The resistivity of the paper stack will vary greatly when equilibrated to other conditions. The experiment would make a good exercise for physics or electronics lab classes. A good question to ask would be: What is the resistivity of one sheet of paper? The photo below shows the Probe measuring the resistance of a Memo Cube paper stack. To calculate the resistivity of the paper stack, multiply the resistance by the electrode area and divide by the thickness of the paper stack. If the measurements are in metres the resistivity will have a unit of ohm metre. Also shown are weights totalling 1.6 kg and a 2,000,000,000 ohm reference resistor inside a plastic box with some drying crystals. Memo Cube Resistivity
## Measurements with teflon tape.To test the probe at higher resistances I used two layers of teflon tape, with a 0.1 mm total thickness covering a 2200 mm^2 tin electrode. The electrodes were connected to the probes by some clip leads. This setup initially produced a 5 minute integration time. Resistance = (5 x 60 / 40) x 5E9 = 3.75E10 ohms. The cell constant was 2200 / 0.1 = 22000 mm or 22 metre.
The resistivity of the teflon tape, plus the probe materials, was 3.75E10 x 22 = On the second day the integration took about took 2 hours. On the third day the integration took about 5 hours.
On the fourth day the integration took about 8 hours.
The resistance can be calculated as 8 x 3600/40 x 5E9 = 3.6E12 ohms.
Multiplying this by 22 metre gives a measured resistivity of
There is no way I can measure the actual |
JEP Related Links Megger-Guide-to-Insulation-Testing Table of Electrical Resistivity and Conductivity The Basics of Low-Current Probing Example Insulation Tester |